Griffiths phase in a facilitated Rydberg gas at low temperatures

The spread of excitations by Rydberg facilitation bears many similarities to epidemics. Such systems can be modeled with Monte Carlo simulations of classical rate equations to great accuracy as a result of high dephasing. Motivated by experiments, we theoretically analyze the dynamics of a Rydberg many-body system in the facilitation regime in the limits of high and low temperatures. In the high-temperature limit, a homogeneous mean-field behavior is recovered, while characteristic effects of heterogeneity can be seen in a frozen gas. At high temperatures, the system displays an absorbing-state phase transition and, in the presence of an additional loss channel, self-organized criticality. In a frozen or low-temperature gas, excitations are constrained to a network resembling an Erdos-Renyi graph. We show that the absorbing-state phase transition is replaced with an extended Griffiths phase, which we accurately describe by a susceptible-infected-susceptible model on the Erdos-Renyi network taking into account Rydberg blockade.